In this section, we compare the performance s of \(T^f_N\)  (natural inclusions; cf. Proposition REF ), \(T^f_C,T^f_M\)  (centered and mixed-centered inclusions; cf. Proposition REF ), \(T^{f_d}_L\)  (decomposition functions proposed in [1]}; cf. Proposition REF ), \(T^{f_d}_{R}\)  (our proposed remainder-form decomposition function in Algorithm REF ), \(T^f_{S_1}\)  (the first proposed bounding approach in [2]}, if applicable), \(T^f_{S_2}\)  (the second proposed approach in [2]}, if applicable) and \(T^{f_d}_{O}\)  (the tight decomposition functions proposed in [4]} for discrete-time and in [5]} for continuous-time systems, when computable; cf. Proposition REF ) in computing the reachable sets of several unconstrained and constrained dynamical systems in the form of (REF ). Further, by the intersection property in Corollary REF , we can also intersect the reachable sets of all applicable inclusion functions (except \(T^{f_d}_{O}\) ) for comparison. Note that we only compare methods in the literature that use first-order (generalized) gradient information. The consideration of higher-order information is a subject of our future work.
